Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20263913 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic199 | C2 | semidirect |
| 5. C2×C4×Dic199 | C2 | semidirect |
| 6. C2×C4⋊C4×C199 | C2 | semidirect |
| 10. C2×C4×D199 | C4 | semidirect |
| 12. C4⋊Dic199 | C22 | semidirect |
| 14. C4×Dic199 | C22 | semidirect |
| 17. C4⋊C4×C199 | C22 | semidirect |
| 26. C4×D199 | C2×C4 | semidirect |
| 44. C2×C199 | #117 | semidirect |
| 49. C199 | C2×#117 | semidirect |
| 54. C2×C4⋊C4 | D199 | semidirect |
| 65. C4⋊C4 | C2×D199 | semidirect |
| 95. C2 | #20263913 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D199 | 2 |
| #20263913 | 2 |
| C2×C4⋊Dic199 | 2 |
| C2×(C2×D199)⋊C4 | 2 |
| C2×C4×Dic199 | 2 |
| C2×C4⋊C4×C199 | 2 |
| C2×#117 | 199 |